Answer:
pounds
Step-by-step explanation:
pounds : ounces
10 : [tex]x[/tex]
1 : 16
[tex]x=160[/tex]
The numerator would be pounds. [tex]\frac{10 pounds}{160 ounces}[/tex]
When we multiply a number by 3, we
sometimes/always/never v
get the same value as if we added 6
to that number.
Stuck? Watch a video or use a hint.
Report a problem
7 of 7 ..
nyone, anywhere
Imnact
Math by grace
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Answer:
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The price of a truck depreciates 15% in a year.
What will be its price in a year if the initial price is
currently 25.000$? -
Answer:
$1.66666667 (or just 1.6)
Step-by-step explanation:
$25.000 US dollars divided by 15 = $1.66666667 US dollars
Consider the line 9x – 7y=-8.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Х
?
Slope of a parallel line:
Answer:
Step-by-step explanation:
Before you can answer you have to solve the equation for y.
Y = 9/7 x+8/7
Parallel lines have the same slope so would also be 9/7
Perpendicular lines have opposite reciprocal slope so would be -7/9
Answer:
y=-9/7x-8/7
Step-by-step explanation:
9x – 7y=-8
-9x -9x
-7y=-9x-8
then divide all sides by -7
y=-9/7x-8/7
Find the acute angle between the diagonal of rectangle whose sides are 5cm and 7cm
Answer:
The arc tangent of angle a = (5/7)
angle a = 35.538 Degrees
Of course, we might be solving for angle b so,
angle b = 90 -35.538 Degrees = 54.462 Degrees
Step-by-step explanation:
During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10miles. A certain county is responsible for repairing potholes in a 30-mile stretch of the interstate. LetXdenote the number of potholes thecounty will have to repair at the end of next winter.
(a) The distribution of the random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the expected value and variance of X.
(c)The cost of repairing a pothole is $5000. If Y denotes the county’s pothole repair expense for next winter, find the mean value and variance Y?
Answer:
a) (iv) Poisson.
b) E(X)=V(X)=λ=4.8
c) E(Y)=24,000
V(Y)=120,000,000
Step-by-step explanation:
We can appropiately describe this random variable with a Poisson distribution, as the probability of having a pothole can be expressed as a constant rate per mile (0.16 potholes/mile) multiplied by the stretch that correspond to the county (30 miles).
The parameter of the Poisson distribution is then:
[tex]\lambda=0.16\cdot 30=4.8[/tex]
b) The expected value and variance of X are both equal to the parameter λ=4.8.
c) If we define Y as:
[tex]Y=5000X[/tex]
the expected value and variance of Y are:
[tex]E(Y)=E(5,000\cdot X)=5,000\cdot E(X)=5,000\cdot 4.8=24,000\\\\\\ V(Y)=V(5000\cdot X)=5000^2\cdot V(X)=25,000,000\cdot 4.8=120,000,000[/tex]
Pls pls pretty pls do any of these whatever you know pls
Answer:
5) 8
6) True, a trapezium has at least 1 parallel side, and a parallelogram has 2.
7) I can't see where angle z is..., but x=42 and y= 96
Step-by-step explanation:
A rhombus has all sides of equal length, thus, if DC is 5, then all the other sides are also 5.
We see that AC is 6, and OC will be 3, or 6/2.
The pythagorean theorem shows that OD is 4, and BD is 8.
42+42=84
180-84=96
Answer:
5. BD = 8 cm
6. See explanation below.
7. x = 42; y = 96; z = 64
Step-by-step explanation:
5.
DC = 5 cm
The diagonals of a rhombus bisect each other, so since AC = 6 cm, OC = 3 cm.
The diagonals of a rhombus are perpendicular to each other, so triangle DOC is a right triangle with right angle DOC.
a^2 + b^2 = c^2
(DO)^2 + (OC)^2 = (DC)^2
(DO)^2 + (3 cm)^2 = (5 cm)^2
(DO)^2 + 9 cm^2 = 25 cm^2
(DO)^2 = 16 cm^2
DO = 4 cm
Since BD = 2DO,
BD = 2(4 cm) = 8 cm
Answer: BD = 8 cm
6.
There are different definitions of trapezium. In the U.S., trapezium is a quadrilateral, none of whose sides are parallel. According to the U.S. definition of trapezium, then, no parallelogram is a trapezium.
According to the UK definition of trapezium, a trapezium is a quadrilateral with at least 2 parallel sides. That means the other two sides may or may not be parallel. According to this definition, then a parallelogram is always a trapezium.
8.
Triangle ADB is isosceles with AD = AB. That meakes their opposite angles congruent.
x = m<ADB = 42
42 + 42 + y = 180
y = 96
In a kite, there are two pairs of congruent sides. DC = BC, so z = m<BDC
z + z + 52 = 180
2z = 128
z = 64
An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and of having a major accident is 0.05 (and these events are mutually exclusive), what is the insurance company's expected profit on the policy
Answer: the expected profit will be $755 annually.
Explanation: Expected Profit (EP) = Charges (income for the insurance company) - probability of minor accidents X amount payable for a minor accident - probability of mayor accidents X amount payable for a major accident.
800- 1000 (0.2) -5000 (0.05)= 800-20-25= 755
Please help me thanks
Answer:
-75 and 75
Step-by-step explanation:
The two numbers chosen or plotted by them are:
-75 and 75
Step-by-step explanation:
It is given that Bernita and Derek each plot a number on a number line with the properties:
1. The two numbers they have plotted are unique or different.
2. Also there absolute value is same.
3. The sum of the absolute values of the numbers is 150.
We know that Absolute value of a positive number is a number itself and absolute value of a negative number is it's inverse.
So the two numbers that satisfy the above three properties are:
-75 and 75.
If a rectangle has a width of 7 centimeters less than it’s length, and it’s area is 330 square centimeters. What are it’s length and width
Answer:
length 22 cmwidth 15 cmStep-by-step explanation:
If we assume the length and width are integer numbers of centimeters, we can look at the factors of 330:
330 = 1×330 = 2×165 = 3×110 = 5×66 = 6×55 = 10×33 = 11×30 = 15×22
The factors in this last pair differ by 7, so represent the width and length of the rectangle.
The rectangle's length and width are 22 cm and 15 cm, respectively.
Solve for x.
x + 3 = Sqrt 4x+17
Answer:
Step-by-step explanation
what is the area of a circle with a radius of 42 in use 3.14 for pi
Answer:
[tex] \boxed{Area \: of \: circle = 5538.96 {in}^{2}} [/tex]
Step-by-step explanation:
Radius (r) = 42 in.
Area of circle = πr²
= 3.14 × (42)²
= 3.14 × 1764
= 5538.96 in²
Which of the following is the result of the operation below?
Answer:
The result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Step-by-step explanation:
The matrix provided is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right][/tex]
The operation to be performed is:
[tex]-R_{1}+R_{2}[/tex] → [tex]R_{2}[/tex]
The operation implies that, we need to replace the values in row 2 by the result of the expression ([tex]-R_{1}+R_{2}[/tex]).
Complete the operation as follows:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right]\rightarrow \ \left[\begin{array}{ccc|c}1&2&3&6\\(-1+1)&(-2+1)&(-3+1)&(-6-2)\\0&2&1&5\end{array}\right][/tex]
[tex]\rightarrow\ \left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Thus, the result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
edge 2021
On her way to work, a commuter encounters four traffic signals. Assume that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection. The first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute.What is the probability that the commuter has to stop at least three times?
Answer:
7 in 36 or 0.1944
Step-by-step explanation:
The probability of having to stop at least three times is the probability of getting 3 or 4 red lights.
For the first two lights, the probability of getting them red is 20 in 60 (1/3).
For the last two lights, the probability of getting them red is 30 in 60 (1/2).
The probability of all of them being red is:
[tex]P(R=4) = \frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}\\P(R=4) =\frac{1}{36}=\frac{1}{36}[/tex]
The probability of three of them being red (3 red + 1 green) is:
[tex]P(R=3) = {(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}}*\frac{1}{2}+(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}\\P(R=3) =2*(\frac{2}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})+2*(\frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})\\ P(R=3) =\frac{4}{36}+\frac{2}{36}\\ P(R=3) =\frac{6}{36}[/tex]
Therefore, the probability of at least three red lights is:
[tex]P=\frac{1}{36}+\frac{6}{36}=\frac{7}{36}\\ P=0.1944[/tex]
The probability is 7 in 36 or 0.1944.
The probability that the commuter has to stop at least three times is at least 5.55%.
Since on her way to work, a commuter encounters four traffic signals, assuming that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection, and the first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute, to determine what is the probability that the commuter has to stop at least three times the following calculation must be performed:
4/6 = 2/3 = 0.66666 0.5 x 0.5 x 0.333 = 0.083333 0.5 x 0.333 x 0.333 = 0.055555
Therefore, the probability that the commuter has to stop at least three times is at least 5.55%.
Learn more in https://brainly.com/question/23273737
What is the sum of 7 3/5 and 2 4/5?
Step-by-step explanation:
[tex]7 \times \frac{3}{5} + 2 \times \frac{4}{5} \\ \frac{38}{5} + \frac{14}{5} \\ \frac{38 + 14}{5} \\ \frac{52}{5} \\ 10 \times \frac{2}{5} [/tex]
Answer:
Step-by-step explanation
7 [tex]\frac{3}{5}[/tex] + 2 [tex]\frac{4}{5}[/tex]
= 38/5 + 14/5
=52/5
If 20% of the people in a community use the emergency room at a hospital in one year, find
the following probability for a sample of 10 people.
a) At most three used the emergency room
b) Exactly three used the emergency room
c) At least five used the emergency room
Answer:
a) 87.91% probability that at most three used the emergency room
b) 20.13% probability that exactly three used the emergency room.
c) 3.28% probability that at least five used the emergency room
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Sample of 10 people:
This means that [tex]n = 10[/tex]
20% of the people in a community use the emergency room at a hospital in one year
This means that [tex]p = 0.2[/tex]
a) At most three used the emergency room
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]
[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]
[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791[/tex]
87.91% probability that at most three used the emergency room
b) Exactly three used the emergency room
[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]
20.13% probability that exactly three used the emergency room.
c) At least five used the emergency room
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
From 0 to 3, we already have in a).
[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672[/tex]
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328[/tex]
3.28% probability that at least five used the emergency room
Suppose that an outbreak of cholera follows severe flooding in an isolated town of 3662 people. Initially (Day 0), 36 people are infected. Every day after, 34% of those still healthy fall ill.
How many people will be infected by the end of day 9?
Answer:
3576 infected people
Step-by-step explanation:
We have to apply the following formula, which tells us the number of healthy people:
A = p * (1 - r / 100) ^ t
where,
p = initial population,
r = rate of change per period (days)
t = number of periods (days)
Now, we know that the initial population is 3,662 but there are already a total of 36 infected, therefore:
3662 - 36 = 3626
that would be our p, now, we replace:
A = 3626 * (1 - 34/100) ^ 9
A = 86.16
Therefore, those infected would be:
3662 - 86.16 = 3575.84
This means that there are a total of 3576 infected people.
The proportion of items in a population that possess a specific attribute is known to be 0.40. If a simple random sample of size 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.46, what is the sampling error?
Answer:
The sampling error = 0.06
Step-by-step explanation:
From the given information:
Let represent [tex]\beta[/tex] to be the population proportion = 0.4
The sample proportion be P = 0.46 &
The sample size be n = 100
The population standard duration can be expressed by the relation:
Population standard duration [tex]\sigma = \sqrt{\dfrac{\beta(1- \beta)}{n}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(1-0.4)}{100}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(0.6)}{100}}[/tex]
[tex]\sigma = 0.049[/tex]
The sample proportion = 0.46
Then the sampling error = P - [tex]\beta[/tex]
The sampling error = 0.46 - 0.4
The sampling error = 0.06
Nancy has to cut out circles of diameter 1 3/ 7 cm from an aluminium strip of dimensions 7 1/ 7 cm by 1 3/ 7 cm . How many full circles can Nancy cut?
Answer:
Nancy can cut 6 full circles
Step-by-step explanation:
Length of aluminium strip = [tex]7 \frac{1}{7} cm[/tex]
Length of aluminium strip =[tex]\frac{50}{7} cm[/tex]
Breadth of aluminium strip =[tex]1 \frac{3}{7} cm[/tex]
Breadth of aluminium strip =[tex]\frac{10}{7} cm[/tex]
Area of strip = [tex]Length \times Breadth = \frac{50}{7} \times \frac{10}{7} =\frac{500}{49}[/tex]
Diameter of circle = [tex]1 \frac{3}{7} cm[/tex]
Diameter of circle = [tex]\frac{10}{7} cm[/tex]
Radius of circle =[tex]\frac{10}{ 7 \times 2}=\frac{10}{14} cm[/tex]
Area of circle =[tex]\pi r^2 = \frac{22}{7} \times (\frac{10}{14})^2=\frac{550}{343} cm^2[/tex]
No. of circles can be cut = [tex]\frac{\frac{500}{49}}{\frac{550}{343}}=6.3636[/tex]
So,Nancy can cut 6 full circles
f(x) = x2 + 1
g(x) = 5-x
(f+g)(x) =
O x2 + x-4
x²+x+4
O x2-x+6
O x2 + x + 6
Answer:
[tex] \boxed{(f + g)(x) = {x}^{2} - x + 6} [/tex]
Given:
[tex]f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x[/tex]
To Find:
[tex](f + g)(x) = f(x) + g(x)[/tex]
Step-by-step explanation:
[tex] = > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6[/tex]
The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 68. If the standard deviation of grades is 15, in what range would you expect 68.26 percent of the grades to fall? (Round answers to 2 decimal places, e.g. 15.25. Hint: Think in terms of what the expected highest and lowest scores would be for 68.26% of the students taking the exam.)
Answer:
The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 68, \sigma = 15[/tex]
Middle 68.26% of the grades:
From the
50 - (68.26/2) = 15.87th percentile
To the
50 + (68.26/2) = 84.13rd percentile.
15.87th percentile:
X when Z has a pvalue of 0.1587. So X when Z = -1.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1 = \frac{X - 68}{15}[/tex]
[tex]X - 68 = -1*15[/tex]
[tex]X = 53[/tex]
84.13rd percentile:
X when Z has a pvalue of 0.8413. So X when Z = 1.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1 = \frac{X - 68}{15}[/tex]
[tex]X - 68 = 1*15[/tex]
[tex]X = 83[/tex]
The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.
4-3 times 54 divided by 9 (Explain)
Answer:
6
Step-by-step explanation:
4-3x54÷9
How I'd do it is separate it:
4-3=1
Then 1x54=54
Then 54/9=6
Answer:
6
Step-by-step explanation:
[tex]4-3*54/9\\4-3 =1\\1*54 =54 \\54/9 =6[/tex]
16. The population of a town is 41732. If there are 19569 male then find the
number of females in the towny
Answer:
The answer is, 22,163
Step-by-step explanation:
Take the total amount of people (41732) and subtract the amount of males (19569) to get your answer.
41732-19569=22,163
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 52.4 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quintuple (5x) the sample size. What is the standard error for the new sample size? Please round your answer to the nearest tenth.
Answer:
The new standard error is [tex]e_{new} = 23.4[/tex]
Step-by-step explanation:
From the question we are told that
The standard error is [tex]e = 52.4[/tex]
Generally the standard error is mathematically represented as
[tex]e = \frac{6}{\sqrt{n} }[/tex]
Where n is the sample size
for the original standard error we have
[tex]52.4 = \frac{6}{\sqrt{n} }[/tex]
Now sample size is quintuple
[tex]e_{new} = \frac{6}{\sqrt{5 * n} }[/tex]
[tex]but \ \ 52.4 = \frac{6}{\sqrt{n} }[/tex]
So [tex]e_{new} = \frac{52.4}{\sqrt{5} }[/tex]
[tex]e_{new} = 23.4[/tex]
Factor completely x3 + 9x2 + 27x+ 27
Answer:
(x + 3)^3
Step-by-step explanation:
I don't exactly know how to break this down into small steps. I can tell you that it is something like (x + a)^3
It turns out that a = 3 because all the signs in the given equation are +
Answer
(x + a) = (x + 3)^3
Mme. Giselle's boutique in Cleveland, Ohio is planning to sell a Parisian frock. If the public view it as being the latest style, the frocks will be worth $10 comma 000. However, if the frocks are viewed as passe, they will be worth only $2 comma 000. If the probability that they are stylish is 10%, what is the expected value of the frocks? The expected value of the frocks (EV) is EVequals$ nothing. (Enter your response rounded to two decimal places.)
Answer:
the expected value of the frocks (EV) is 2800
Step-by-step explanation:
the expected value of the frocks= (probability of stylish* worth)+(probability of passe* worth)
If the public view it as being the latest style, the frocks will be worth $10,000.
if the frocks are viewed as passe, they will be worth only $2,000.
If the probability that they are stylish is 10%
probability of stylish = 10000
worth = 10%
probability of passe = 2000
[tex]=10 \%*10000+(1-10 \%)*2000\\\\=0.1\times 10000+(1-0.1)\times2000\\\\=1000+(0.9)\times2000\\\\=1000+1800\\\\=2800[/tex]
Therefore, the expected value of the frocks (EV) is 2800
what is a acute?? i dont really seem to get it
Answer:
an angle less than 90 degrees
Step-by-step explanation:
so like this angle /_
this is obtuse \_
this is right |_
Find the probability of the indicated event if P(E)equals0.25 and P(F)equals0.40. Find P(E or F) if P(E and F)equals0.05.
Answer:
[tex] P(E) =0.25, P(F) = 0.40, P(E \cap F) =0.05[/tex]
[tex] P(E \cup F)= P(E) +P(F) -P(E \cap F)[/tex]
And replacing we got:
[tex] P(E \cup F)=0.25 +0.40 -0.05 = 0.6[/tex]
Step-by-step explanation:
For this case we have the following probabilities given:
[tex] P(E) =0.25, P(F) = 0.40, P(E \cap F) =0.05[/tex]
And we want to find this probability:
[tex] P(E \cup F)[/tex]
And we can use the total probability rule given by:
[tex] P(E \cup F)= P(E) +P(F) -P(E \cap F)[/tex]
And replacing we got:
[tex] P(E \cup F)=0.25 +0.40 -0.05 = 0.6[/tex]
When dots are printed from a laser printer to form letters, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion of your eye at distances typical for reading Randomized Variables D 2.5 mm d-38 cm Take the pupil of the eye to be 2.5 mm in diameter and the distance from the paper to the eye as 38 cm. Find the minimum separation of two dots such that they cannot be resolved in cm. Assume a wavelength of 555 nm for visible light.
Answer:
The minimum separation is [tex]z = 1.0292 *10^{-4} \ m[/tex]
Step-by-step explanation:
From the question we are told that
The reading randomized variable are [tex]D= 2.5 \ mm[/tex] and [tex]d = 38 \ cm[/tex]
The diameter of the pupil is [tex]d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m[/tex]
The distance from the paper is [tex]D = 38 \ cm = 0.38 \ m[/tex]
The wavelength is [tex]\lambda = 555 \ nm = 555 * 10 ^{-9} m[/tex]
Generally the Raleigh's equation for resolution is
[tex]\theta = 1.22 [\frac{\lambda}{D} ][/tex]
substituting values
[tex]\theta = 1.22 * \frac{555*10^{-9}}{0.0025}[/tex]
[tex]\theta = 2.7084*10^{-4} \ rad[/tex]
The minimum separation of two dots is mathematically represented as
[tex]z = \theta d[/tex]
substituting values
[tex]z = 2.7084*10^{-4} * 0.38[/tex]
[tex]z = 1.0292 *10^{-4} \ m[/tex]
Which is the vertex of x^2 + 10x = - 17?
Answer:
(-5, -8)
Step-by-step explanation:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).
x^2 + 10x = - 17
x^2+10x+17=0
x^2+2*5x+25 - 8=0
(x+5)^2-8=0
h=-5, k= -8
vertex is (-5, -8)
5500 milliliters equal how many liters show work
Answer:
5.5 liters
Step-by-step explanation:
1 milliliter equals to 1/1000 part of a liter, which is 0.001 liter.
1 milliliter = 1 * 0.001 liter
So if you have 5500 milliliters that means it equals to 5500 times one milliliters and 1 milliliter = 1 * 0.001 liter, so for 5500 milliliters it is 5500 times as much
5500 * 0.001
5500 * 1/1000
5500 / 1000
5.5 liters
As long as you know this number 0.001 , then it is easily to calculate between liters and milliliters.
EXTRA:
To convert from amount A which is given in a certain quantity, to another quantity, you sometimes have to multiply and in other cases you need to divide by a certain factor. The factor defines the relationship between the quantities.
Suppose you have 1000 times 1 milliliter then you can find the amount in liters by multiplying that number of milliliters times 0.001.
It is easy to see that
1000 * 1/1000
1000 / 1000
= 1 liter, but that is easy, because I choose an easy number for the amount of milliliters to convert into liters. But it works exactly the same for any amount!